Maximum Matching Algorithm Research Articles

The Locality of Distributed Symmetry Breaking

Symmetry-breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open. In this article we work in the LOCAL model (where the input graph and underlying distributed network are identical) and study the randomized complexity of four fundamental symmetry-breaking problems on graphs: computing MISs (maximal independent sets), maximal matchings, vertex colorings, and ruling sets. A small sample of our results includes the following: —An MIS algorithm running in O (log 2 Δ + 2 o (√log log n ) ) time, where Δ is the maximum degree. This is the first MIS algorithm to improve on the 1986 algorithms of Luby and Alon, Babai, and Itai, when log n ≪ Δ ≪ 2√log n , and comes close to the Ω(log Δ / log log Δ lower bound of Kuhn, Moscibroda, and Wattenhofer. —A maximal matching algorithm running in O (log Δ + log 4 log n ) time. This is the first significant improvement to the 1986 algorithm of Israeli and Itai. Moreover, its dependence on Δ is nearly optimal . —A (Δ + 1)-coloring algorithm requiring O (log Δ + 2 o (√log log n ) time, improving on an O (log Δ + √log n )-time algorithm of Schneider and Wattenhofer. —A method for reducing symmetry-breaking problems in low arboricity/degeneracy graphs to low-degree graphs. (Roughly speaking, the arboricity or degeneracy of a graph bounds the density of any subgraph.) Corollaries of this reduction include an O (√log n )-time maximal matching algorithm for graphs with arboricity up to 2√log n and an O (log 2/3 n )-time MIS algorithm for graphs with arboricity up to 2 (log n )1/3 . Each of our algorithms is based on a simple but powerful technique for reducing a randomized symmetry-breaking task to a corresponding deterministic one on a poly(log n )-size graph.

A matrix-algebraic formulation of distributed-memory maximal cardinality matching algorithms in bipartite graphs

We describe parallel algorithms for computing maximal cardinality matching in a bipartite graph on distributed-memory systems. Unlike traditional algorithms that match one vertex at a time, our algorithms process many unmatched vertices simultaneously using a matrix-algebraic formulation of maximal matching. This generic matrix-algebraic framework is used to develop three efficient maximal matching algorithms with minimal changes. The newly developed algorithms have two benefits over existing graph-based algorithms. First, unlike existing parallel algorithms, cardinality of matching obtained by the new algorithms stays constant with increasing processor counts, which is important for predictable and reproducible performance. Second, relying on bulk-synchronous matrix operations, these algorithms expose a higher degree of parallelism on distributed-memory platforms than existing graph-based algorithms.We report high-performance implementations of three maximal matching algorithms using hybrid OpenMP-MPI and evaluate the performance of these algorithm using more than 35 real and randomly generated graphs. On real instances, our algorithms achieve up to 200 ? speedup on 2048 cores of a Cray XC30 supercomputer. Even higher speedups are obtained on larger synthetically generated graphs where our algorithms show good scaling on up to 16,384 cores.

A Case-Based Reasoning System to Control Traffic at Signalized Intersections

Traffic control systems (TCS) contribute to relieve congestion in cities. Although many optimization and intelligent approaches exist to develop TCS, only a few works have investigated Case Based Reasoning (CBR) to control traffic at signalized intersections. Existing works usually state that the case-base is created using experts’ knowledge but do not specify how this knowledge is acquired and how the case-base is built. In this article, we design a CBR system to control traffic at a single signalized intersection. We develop a hybrid methodology to create the case-base using simulation-optimisation, Condensed Nearest Neighbour algorithm (CNN) and a rule-based system. The algorithm is implemented in Python and applied on an intersection simulated using VISSIM, a state-of-the-art traffic simulation software. The performance of the system is assessed and compared to the Longest Queue First with Maximal Weight Matching (LQF-MWM) algorithm. Results show that the implemented system is able to handle different traffic scenarios with competitive performance.

Greedy Matching: Guarantees and Limitations

Since Tinhofer proposed the MinGreedy algorithm for maximum cardinality matching in 1984, several experimental studies found the randomized algorithm to perform excellently for various classes of random graphs and benchmark instances. In contrast, only few analytical results are known. We show that MinGreedy cannot improve on the trivial approximation ratio of $$\frac{1}{2}$$12 whp., even for bipartite graphs. Our hard inputs seem to require a small number of high-degree nodes. This motivates an investigation of greedy algorithms on graphs with maximum degree $$\varDelta $$Δ: we show that MinGreedy achieves a $${\frac{{\varDelta }-1}{2{\varDelta }-3}} $$Δ-12Δ-3-approximation for graphs with $${\varDelta } {=} 3$$Δ=3 and for $$\varDelta $$Δ-regular graphs, and a guarantee of $${\frac{{\varDelta }-1/2}{2{\varDelta }-2}} $$Δ-1/22Δ-2 for graphs with maximum degree $${\varDelta } $$Δ. Interestingly, our bounds even hold for the deterministic MinGreedy that breaks all ties arbitrarily. Moreover, we investigate the limitations of the greedy paradigm, using the model of priority algorithms introduced by Borodin, Nielsen, and Rackoff. We study deterministic priority algorithms and prove a $${\frac{{\varDelta }-1}{2{\varDelta }-3}}$$Δ-12Δ-3-inapproximability result for graphs with maximum degree $${\varDelta } $$Δ; thus, these greedy algorithms do not achieve a $$\frac{1}{2} {+} \varepsilon $$12+?-approximation and in particular the $$\frac{2}{3}$$23-approximation obtained by the deterministic MinGreedy for $${\varDelta } {=} 3$$Δ=3 is optimal in this class. For k-uniform hypergraphs we show a tight $$\frac{1}{k}$$1k-inapproximability bound. We also study fully randomized priority algorithms and give a $$\frac{5}{6}$$56-inapproximability bound. Thus, they cannot compete with matching algorithms of other paradigms.

A QOS Based Load Balanced Switch

The simple architecture with high forwarding capacity bandwidth is load balancing switch is build with two stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow in the order of load balanced two stage switch. Before load balancing two stages has perform with the Full frame first algorithm and use centralized scheduler to eliminate those mis sequencing problemsand getting the 100% throughput result. There comes at some additional cost and needs costly online scheduling algorithms and need for a complex scheduler and quality being reduced. In this paper we introduce the two stage switch fabric with round robin scheduling algorithmis used to solve mis sequencing problems and two maximum weight matching algorithms Longest queue first(LQF) and Oldest cell first(OCF) to achieve 100% throughput results. Theoretical analysis and simulation results shows that using these algorithms, achieve all the possible outcome results in the switch. � The simple architecture with the load balancing scheme perform with interesting two different stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow to the destination path in the order of load balanced two stage switch fabric. The two stage load balancing switch is more scalable than the any other switch in the network architecture. Hardly load balanced switch got some problem with that, on sending and receiving the data in wired or wireless networks(8), the major problem with that is mis sequencing problems has arised to loss of data packets or mis matched data formats. Somehow in earlier they are tired to clear those problems with the algorithms named, Full frame first algorithm to get mis sequencing problems and they put the centralized schedular to achieve the 100% throughput results(4)(2) in their data packets.Oftenly they got the perfect data packets arrival in destination, but the problem with that methodology is the quality of data is reduced to lower. And manually they they need costly online scheduling algorithms to rectify the mis matching of data and need more complex schedular to achieve the 100% throughput result of outcome data. We introduce in this paper to rectify the mis sequencing problems(1) and avoid the costly online scheduling algorithms, we use Round robin scheduling algorithms(RRS) to rectify the mis matching of data packets in the tcp applications and two maximum weight matching algorithms namely, Longest queue first(LOQ) and Oldest cell first(OCF) to achieve 100% throughput result for all independent arrival packets.(11)These algorithms are used to eliminate the complex schedular and needs of online costly scheduling algorithm to schedule the data packets in the destination node. The another approach of this proposed is to get the high quality of data packets in destination node which is the data which is send by sender, the receiver also got the same quality of data(9) without defragmentation and reduction of quality. We observed that in the algorithms and methodolgy of using those above like, RRS, LOQ and OCF, not only to solve mis sequencing problems and also get quality of data packets service of the same aaplication(10). Yet we are consider more algorithm to get the quality of data packets. Our idea is to just keep packets

Research on Chinese Natural Language Query Interface to Database Based on Syntax and Semantic

The query of database must rely on professional query language, which is difficult to grasp for ordinary users. Natural language query interface (NLQI) can be applied to solve this problem with better human-computer interaction and intelligence. However, current natural language understanding technology is not mature. Though the query sentences’ structure is fixed, it is also difficult to accurately convert query sentences into understandable database query language for computer. Therefore a method of designing NLQI based on syntax and semantic analysis is proposed in this paper. First of all, Maximum forward and maximum reverse matching algorithms are used to analyse sentence by part of speech (POS) template, which is able to demonstrate the syntax relationship among the words. After syntax analysis, query conditions and targets are identified. Then, single conditions and targets are analyzed to relative standard forms by the relationship among entity, property, connect verb and unit. At last, these standard forms are transformed to SQL sentence. Regarding printing ERP system as experimental subject, experiment is done in this paper. The result shows that the method proposed in this paper can meet the needs of natural language query, and has a good transform effect for combination, omitting and other complex sentences.

Expected time complexity of the auction algorithm and the push relabel algorithm for maximum bipartite matching on random graphs

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We first prove that if for every non-maximum matching on graph G there exist an augmenting path with a length of at most 2l + 1 then the auction algorithm converges after N ⋅ l iterations at most. Then, we prove that the expected time complexity of the auction algorithm for bipartite matching on random graphs with edge probability and c > 1 is w.h.p. This time complexity is equal to other augmenting path algorithms such as the HK algorithm. Furthermore, we show that the algorithm can be implemented on parallel machines with processors and shared memory with an expected time complexity of . © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 384–395, 2016

On efficient implicit OBDD-based algorithms for maximal matchings

The maximal matching problem, i.e., the computation of a matching that is not a proper subset of another matching, is a fundamental optimization problem, and maximal matching algorithms have been used as submodules for problems like maximal node-disjoint paths or maximum flow. Since in some applications very large graphs have to be processed, a research branch has emerged which is concerned with the design and analysis of implicit algorithms for classical graph problems. Input graphs are given as characteristic Boolean functions of their edge sets, and problems have to be solved by functional operations. As OBDDs, which are closely related to deterministic finite automata, are a well-known data structure for Boolean functions, OBDD-based algorithms are used as a heuristic approach to handle very large graphs. Here, an implicit OBDD-based maximal matching algorithm is presented that uses only a polylogarithmic number of functional operations with respect to the number of vertices of the input graph. In order to investigate the algorithm's behavior on large and structured networks, it is analyzed on grid graphs. It is shown that the overall running time and the space requirement is also polylogarithmic. Furthermore, we present another algorithm similar to the well-known Karp–Sipser approach and we investigate the representation size of maximal matchings.

Bidirectional Maximal Matching Word Segmentation Algorithm with Rules

Bidirectional maximum matching algorithm (BMM) combined positive maximal matching and reverse maximal matching algorithm, it was a more commonly used word segmentation method now, but it was low efficient and couldn’t solve the ambiguity. Therefore, an improved method was proposed combining with improved dictionary structure, and changing maximal matching word length dynamically to improve the efficiency of word segmentation. In order to get the correct segmentation results, we also proposed several rules. Compared with traditional segmentation methods, it proves that bidirectional maximal matching word segmentation with rules has higher speed and precision.

Improved Backtracking-Forward Algorithm for Maximum Matching Chinese Word Segmentation

In order to improve the accuracy of segmentation, analysis of backtracking-forward maximum matching algorithm exists two defects when dealing with crossing ambiguity, and on this basis, an improved-backtracking forward algorithm for maximum matching algorithm is presented. The improved algorithm is based on the backtracking-forward maximum matching algorithm and adds a module, a chain length of one and 3-words, that can detect and process crossing ambiguity, and taking advantage of counting method, we can merely sort out the defragmenter fields that occurred crossing ambiguity. A number of selected language corpus tests prove that under the premise of the segmentation speed, the improved algorithm can enhance the segmentation accuracy.

On parallel push–relabel based algorithms for bipartite maximum matching

We study multithreaded push–relabel based algorithms for computing maximum cardinality matching in bipartite graphs. Matching is a fundamental combinatorial problem with applications in a wide variety of problems in science and engineering. We are motivated by its use in the context of sparse linear solvers for computing the maximum transversal of a matrix. Other applications can be found in many fields such as bioinformatics (Azad et al., 2010) [4], scheduling (Timmer and Jess, 1995) [27], and chemical structure analysis (John, 1995) [14]. We implement and test our algorithms on several multi-socket multicore systems and compare their performance to state-of-the-art augmenting path-based serial and parallel algorithms using a test set comprised of a wide range of real-world instances. Building on several heuristics for enhancing performance, we demonstrate good scaling for the parallel push–relabel algorithm. We show that it is comparable to the best augmenting path-based algorithms for bipartite matching. To the best of our knowledge, this is the first extensive study of multithreaded push–relabel based algorithms. In addition to a direct impact on the applications using matching, the proposed algorithmic techniques can be extended to preflow-push based algorithms for computing maximum flow in graphs.

Geo-Visualization of Agricultural Products Price Data Based on WebGIS

In China, there is a large amount of data about agricultural products price released by thousands of agricultural websites on the Internet. These records are basically displayed in the form of text, table, and statistics chart but location information cannot be displayed graphically. Rich client and WebGIS techniques can improve representation of agricultural products price and help to provide effective technological solutions for increasing data. First, we describe the methods of standardizing agricultural products price data, which is crawled from agricultural websites through vertical search engine. Forward maximum matching algorithm is then explained and applied for spatializing data. After that, technologies of WebGIS based on rich client (JavaScript/Ajax and Flex) are summarized and analyzed and the map visualization methods of agricultural products price are presented, taking Baidu Map API and ArcGIS API for Flex for example. The methods can provide visual, interactive, user-friendly representation of agricultural products price data in geography information system as well as share visualization services through Internet or Intranet to improve data exchange and utilization. Compared to traditional WebGIS, WebGIS based on RIA improves user satisfaction and increases response speed. The results demonstrate that WebGIS by using RIA technology is a feasible solution method for map visualization of agricultural products price.

A Parallel Maximal Matching Algorithm for Large Graphs Using Pregel

Graph matching is to find an independent edge set in a graph. It can be used for various purposes such as finding a cover in a graph, chemical structural computations, multi-level graph partitioning and so on. When a graph is too large to be handled by a single machine, we should use multiple machines. In this paper, we use Pregel, a cloud graph processing architecture which is able to process massive scale graph data in scalable and fault-tolerant ways. We propose a parallel maximal matching algorithm described in the Pregel's vertex-centric BSP model. We test our algorithm on an 8 node cluster and the results show that our algorithm can realize high quality matching for a large graph in a short time. Also, our algorithm is linearly scalable with the number of machines.

On matching cover of graphs

A k-matching cover of a graph $$G$$ G is a union of $$k$$ k matchings of $$G$$ G which covers $$V(G)$$ V ( G ) . The matching cover number of $$G$$ G , denoted by $$mc(G)$$ m c ( G ) , is the minimum number $$k$$ k such that $$G$$ G has a $$k$$ k -matching cover. A matching cover of $$G$$ G is optimal if it consists of $$mc(G)$$ m c ( G ) matchings of $$G$$ G . In this paper, we present an algorithm for finding an optimal matching cover of a graph on $$n$$ n vertices in $$O(n^3)$$ O ( n 3 ) time (if use a faster maximum matching algorithm, the time complexity can be reduced to $$O(nm)$$ O ( n m ) , where $$m=|E(G)|$$ m = | E ( G ) | ), and give an upper bound on matching cover number of graphs. In particular, for trees, a linear-time algorithm is given, and as a by-product, the matching cover number of trees is determined.

Optimal bit complexity randomised distributed MIS and maximal matching algorithms for anonymous rings

We present and analyse Las Vegas distributed algorithms which compute a MIS or a maximal matching for anonymous rings. Their bit complexity and time complexity are O(logn) with high probability. These algorithms are optimal modulo a multiplicative constant. Beyond the complexity results, the interest of this work stands in the description and the analysis of these algorithms which may be easily generalised. Furthermore, these results show a separation between the complexity of the MIS problem (and of the maximal matching problem) on the one hand and the colouring problem on the other. Colouring can be computed only in Ω(logn) rounds on rings with high probability, while MIS is shown to have a faster algorithm. This is in contrast to other models, in which MIS is at least as hard as colouring.

Research on the Optimal Layout Problem for NC Machining Based on Improved Genetic Algorithm

In the process of NC machining, the optimization processing of graphic layout is a well-studied problem which has practical application value for improving the utilization rate of raw materials and saving the cost of production. In this paper, a new design of genetic algorithm (GA) is proposed for solving this problem. This improved genetic algorithm combines GA with the improved crossover operator and mutation operator. Moreover, the best individual preservation method is integrated into the algorithm. The improved genetic algorithm expands the search space and enhances the GA’s search capabilities. Furthermore, the maximum matching algorithm is proposed based on the lowest horizontal line algorithm, which effectively avoids blind elevating horizontal lines and improves the utilization rate of the lowest horizontal line. It is integrated with the improved genetic algorithm to solve the two-dimensional rectangular parts optimal layout problem which combines the advantages of two kinds of algorithms. The experimental results show that the algorithm can get a good optimization result. DOI: http://dx.doi.org/10.11591/telkomnika.v11i11.3554 Full Text: PDF

A reduction algorithm for the weighted stable set problem in claw-free graphs

In this article the Lovász–Plummer clique reduction is extended to the weighted case and used to find a maximum weight stable set in a claw-free graph G with n nodes in O(n2(n2+L(n))) time, where L(n) is the complexity of finding a maximum weight augmenting path in a line graph H with n nodes. The best algorithm known to date to solve the latter problem is Gabow’s maximum weight matching algorithm (applied to the root graph of H) which has a complexity of O(n2logn). It follows that our algorithm can produce a maximum weight stable set in a claw-free graph in O(n4logn) time.

On the Relevance of Sophisticated Structural Annotations for Disulfide Connectivity Pattern Prediction

Disulfide bridges strongly constrain the native structure of many proteins and predicting their formation is therefore a key sub-problem of protein structure and function inference. Most recently proposed approaches for this prediction problem adopt the following pipeline: first they enrich the primary sequence with structural annotations, second they apply a binary classifier to each candidate pair of cysteines to predict disulfide bonding probabilities and finally, they use a maximum weight graph matching algorithm to derive the predicted disulfide connectivity pattern of a protein. In this paper, we adopt this three step pipeline and propose an extensive study of the relevance of various structural annotations and feature encodings. In particular, we consider five kinds of structural annotations, among which three are novel in the context of disulfide bridge prediction. So as to be usable by machine learning algorithms, these annotations must be encoded into features. For this purpose, we propose four different feature encodings based on local windows and on different kinds of histograms. The combination of structural annotations with these possible encodings leads to a large number of possible feature functions. In order to identify a minimal subset of relevant feature functions among those, we propose an efficient and interpretable feature function selection scheme, designed so as to avoid any form of overfitting. We apply this scheme on top of three supervised learning algorithms: k-nearest neighbors, support vector machines and extremely randomized trees. Our results indicate that the use of only the PSSM (position-specific scoring matrix) together with the CSP (cysteine separation profile) are sufficient to construct a high performance disulfide pattern predictor and that extremely randomized trees reach a disulfide pattern prediction accuracy of on the benchmark dataset SPX, which corresponds to improvement over the state of the art. A web-application is available at http://m24.giga.ulg.ac.be:81/x3CysBridges.

Solving Capacitated Dominating Set by using covering by subsets and maximum matching

The Capacitated Dominating Set problem is the problem of finding a dominating set of minimum cardinality where each vertex has been assigned a bound on the number of vertices it has capacity to dominate. Cygan et al. showed in 2009 that this problem can be solved in O(n3mnn/3) or in O∗(1.89n) time using maximum matching algorithm. An alternative way to solve this problem is to use dynamic programming over subsets. By exploiting structural properties of instances that cannot be solved fast by the maximum matching approach, and “hiding” additional cost related to considering subsets of large cardinality in the dynamic programming, an improved algorithm is obtained. We show that the Capacitated Dominating Set problem can be solved in O∗(1.8463n) time.

Real-Time Path Planning for Coordinated Transport of Multiple Particles Using Optical Tweezers

Automated transport of multiple particles using optical tweezers requires real-time path planning to move them in coordination by avoiding collisions among themselves and with randomly moving obstacles. This paper develops a decoupled and prioritized path planning approach by sequentially applying a partially observable Markov decision process algorithm on every particle that needs to be transported. We use an iterative version of a maximum bipartite graph matching algorithm to assign given goal locations to such particles. We then employ a three-step method consisting of clustering, classification, and branch and bound optimization to determine the final collision-free paths. We demonstrate the effectiveness of the developed approach via experiments using silica beads in a holographic tweezers setup. We also discuss the applicability of our approach and challenges in manipulating biological cells indirectly by using the transported particles as grippers.